CPhill

The probability is  = (1/4) * (1/4)   =   1 / 16

n  is given by :

[375 + 1] / 2  =

376 / 2   =  188

So.....the sum of the series  =

188²  = 35344

 ( [4500 / 2250]  - 1 ) x 100%  =  

(2 - 1) x 100%   =

1 x 100%  = 100%

The bufget would be increased by 100%   [ or, in this case, doubled] 

15mod26   = 15

So....the multiplicative inverse of this = 1/15

Let N be the cost of the meal before the tip and we have that :

N * 1.15 = 27.60     divide both sides by 1.15

N = 27.60 / 1.15 =   24.00

(x + 4)² = 77²       using the square root property, we have

x +  4   =  ± 77

So either

x + 4 =  77     and x = 73

or

x + 4 = -77 and x = -81

So....the answers are   x = 73   and x = -81

We have these points on the total cost graph (0, 100000)   and (1000, 200000).....the slope of this line =

[200000 - 100000] / [ 1000 - 0]  =    100000/1000   = 100

So....the equation  of the line can be found using the point-slope form :

y - 100000  = 100[x - 0]      simplify

y = 100x + 1000000

tan x = √3

We can do this in several ways.......one way is to take the tangent inverse [arctan] of √3.......so we have

arctan √3   =  60°  =  pi/3

This is  also true at 240°  =  4pi/3

We can find the change thusly :

-5 - (-80)  =

-5  + 80  =

75 feet

Let N be the number

Then   27% of N  = 5......so......

.27*N  = 5     divide both sides by .27

N = 5 / .27   = 18.5185  (185 repeating)